Cooperative Resource Allocation in OFDM-Based

Multicell Cognitive Radio Systems

Qianyu Yang, Shaowei Wang & Mengyao Ge

School of Electronic Science and Engineering

Nanjing University, Nanjing 210093, China

E-mail: yqyhzau@126.com, wangsw@nju.edu.cn, mengyao89@yahoo.cn

AbstractIn this paper, we investigate the resource alloca-tion problem for an orthogonal frequency division multiplexing(OFDM) based multicell cognitive radio (CR) system. Secondaryusers (SUs) served by the CR system distribute randomly inmultiple cells and share radio spectrum with primary users(PUs) in a licensed system, where the interference introducedto the PUs must be kept below their tolerable thresholds. In oursystem model, SUs in different CR cells can transmit signalswith the same OFDM subchannel, so cochannel interferenceamong the SUs should also be considered. We propose an efficientalgorithm, named as multi-level waterfilling (MLWF), to allocatepower among OFDM subchannels for all CR cells by jointlyconsidering transmission power and interference constraints. TheMLWF always allocates much power to a subchannel whichgenerates less interference to the PUs. Simulation results showthat our proposed algorithm provides better performance thanother existing ones. Moreover, the complexity of the MLWF ismuch lower than other representative algorithms.

Index TermsCognitive radio, Cooperative resource alloca-tion, OFDM, Optimization

I. INTRODUCTION

Spectrum scarcity becomes a severe problem as the rapid de-

velopment of wireless service demand. However, in despite of

the looming spectrum shortage crisis, investigations show that

radio spectrum is far away from fully utilized [1]. Although

radio spectrum has already been assigned to licensed primary

users (PUs), part of them is usually unused at a certain time

or location. That is to say, spectrum holes exist in both time

and location. In order to fulfill the requirements of spectrum-

hungry applications, cognitive radio (CR) is brought up [2, 3]

and attracts more and more attention in the past ten years [4].

On the other hand, to prohibit the performance degeneration

of the PUs, the interference generated by the SUs must be

regularly controlled. Hence, the physical layer of CR systems

should be very flexible to meet these requirements.

Orthogonal frequency division multiplexing (OFDM) has

been considered as an appropriate modulation scheme for CR

systems [5], owing to its high flexibility in dynamic resource

allocation. A heuristic algorithm called Max-Min is proposed

in [6]. Simulation results show its performance is close to

the optimal, but the computational cost is relatively high. A

simple but fast efficient algorithm is implemented in [7] by

introducing a normalized index to measure the ability of a

subchannel to carry bits. It achieves performance close to the

optimal with a very low computational complexity. However,

both of the algorithms in [6] and [7] are only suitable for

single cell scenario.

For the single cell scenario, SUs are generally assumed

to transmit signals on different subchannels simultaneously.

Nevertheless, for multicell case, it is more reasonable to allow

that SUs in different cells use the same subchannel simulta-

neously [810]. In [8], a distributed algorithm is proposed

to maximize the throughput of the considered CR system

while guaranteeing the rates of nominal users. In [9], a

fully distributed subchannel selection and power allocation

algorithm is proposed by combining an unconstrained opti-

mization method with a constrained partitioning procedure.

However, interference introduced to PUs is not considered

in [8, 9]. In [10], a greedy-like heuristic method, referred to

as multicell Max-Min algorithm, is proposed to solve the

resource allocation problem in multicell CR networks. The

computational complexity of the proposed algorithm is very

high because it has to solve a set of nonlinear equations during

each iteration.

In this paper, we focus on the resource allocation in the

downlink of a multicell OFDM-based CR system and try

to maximize the overall data rate of the SUs. Firstly, we

give a greedy-like water-filling procedure to load bits for

subchannels. Each CR user greedily loads bits on a subchannel

based on its signal to interference plus noise ratio (SINR).

The MLWF applies a simple cooperative adjustment procedure

after the greedy waterfilling algorithm, which can reduce both

cochannel interference and mutual interference. By coopera-

tively moving bits from the subchannels which generates high

interference to the subchannels with lower interference, the

MLWF makes an effort to reduce the capacity loss caused

by the greedy-like algorithms. Simulation results show our

proposed algorithm has a better performance with remarkable

lower complexity compared to other existing methods.

The rest of this paper is organized as follows. Section II

describes system model and formulates the optimization prob-

lem. In III, proposed algorithm is shown in detail. Simulation

results and analysis are presented in Section IV. Conclusion is

drawn in Section V.

II. SYSTEM MODEL AND PROBLEM FORMULATION

A. System Model

Consider that multiple OFDM-based CR cells share spec-

trum with a licensed system. Each CR cell locates a base

2013 International Conference on Computing, Networking and Communications, Cognitive Computing and NetworkingSymposium

978-1-4673-5288-8/13/$31.00 2013 IEEE 724

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Secondary BS1

PU2BS

Primary networkPU1

SU

Secondary BS2SU

Fig. 1. System model: Coexistence of primary and secondary cells

station (BS) and serves an SU. Fig.1 shows the system model

considered in this work. We consider the downlink of the CR

system in this work and try to maximize the sum throughput of

the SUs served by CR cells. We assume that perfect channel-

state information (CSI) is available by channel estimation at

the receiver side, and the CSI is also available at each CR

cells transmission side by feedback. Perfect CSI between

the secondary BSs and a specified PU is also available by

searching the database or sensing the channel.

The primary BS transmits to L PUs. The whole availablespectrum is divided into N subchannels with equal bandwidthB and the starting frequency is fs. There are M CR cells andeach cell is permitted to employ the N subchannels. Let N :={1, 2, . . . , N}, L := {1, 2, . . . , L}, M := {1, 2, . . . ,M}denote the set of subchannels, PUs and CR cells, respectively.

The nominal spectrum of subchannel n, n N , ranges fromfs+(n1)B to fs+nB. The PU ls nominal band is supposedto span from fPUl to f

PUl + Bl, where f

PUl is the starting

frequency and Bl is the occupied bandwidth of PU l, l L.The power spectrum density (PSD) of the OFDM subchan-

nel n used by an SU can be expressed as

SUn (f) = Ts

(

sinfTsfTs

)2

, (1)

where Ts is the symbol duration. The interference introducedto the PU l from CR cell ms BS on subchannel n with unittransmit power is

ISPm,l,n =

fPUl fs(n1

2)B+Bl

fPUl

fs(n1

2)B

gSPm,l,nSUn (f)df, (2)

where gSPm,l,n is the power gain from the CR cell ms BS tothe PU ls receiver on subchannel n.

On the other hand, assume the primary BS casts unit power

on subchannel n, the interference introduced to the SU in CRcell m on subchannel n is

IPSl,m,n =

fs+nBfPUl

1

2Bl

fs+(n1)BfPUl 1

2Bl

gPSn,mPUl (f)df, (3)

where gPSn,m is the power gain on subchannel n from primaryBS to the SU served in CR cell m. PUl (f) is the PSD of PUls signal.Since the primary network and CR network coexist in sys-

tem, there are two kinds of interference introduced to the SUs.

First, cochannel interference between CR cells arises when

multiple SU in different CR cells use the same subchannel.

That is to say, the signal of one CR cell is treated as interfer-

ence by other CR cells transmitting on the same subchannel.

On the other hand, the PUs also generate interference to the

subchannels. Let ISSm,n denote the interference to the SU of themth CR cell on the nth subchannel introduced by the otherCR cells,

ISSm,n =

j 6=m,jM

pjngSSj,m,n, (4)

where pjn is the CR cell js transmit power on subchannel nand gSSj,m,n is power gain from CR cell js BS to CR cell msuser.

The SINR of SU served in the CR cell m on subchannel ncan be defined as

Hm,n = gSSm,m,n/(

2 + IPSm,n + ISSm,n), (5)

where 2 denotes the additive white gaussian noise variance.And IPSm,n is the total interference from PUs to the subchanneln of SU served in CR cell m. From (3), it can be calculatedby

IPSm,n =L

l=1

plnIPSl,m,n, (6)

where pln is the PU ls signal power on subchannel n.The achievable transmission rate on the nth subchannel of

the mth CR cell is

rm,n = B log2 (1 + (pm,nHm,n)/) , (7)

where is the SINR gap.

B. Problem Formulation

The optimization objective is to maximize the sum capacity

of the CR cells which operate in a power-limited situation,

while keeping the interference to the PUs not exceeding spec-

ified thresholds{

IUl , l = 1, 2, . . . , L}

. Thus, the constrained

optimization problem can be formulated as follows,

maxM

m=1

Nn=1 rm,n

s.t. C1 :N

n=1 pm,n Pm, pm,n 0, m M

C2 :M

m=1

Nn=1 pm,nI

SPm,l,n I

Ul , l L.

(8)

The C1 is the power constraint of the mth CR cell. Pmis the maximum transmit power. The C2 are the interferenceconstraints, where the interference threshold of PU l is IUl ,l L.

III. THE PROPOSED ALGORITHM

The optimization problem formulated in (8) is a nonlinear

programming coupling in the constraint C2 which poses aprohibitive computational burden to the system and is gener-

ally very hard to solve. In [11], an iterative waterfilling (IWF)

algorithm yields a nash equilibrium if we regard the resource

allocation problem as a non-cooperative game. Although the

complexity of the IWF algorithm is much less than that of

the exhaustive search algorithm and converges fast in various

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network scenarios, it has sub-optimal performance with greedy

criterion.

To address limitations of IWF, many other methods have

been proposed. In [10], a heuristic algorithm called multicell

Max-Min is proposed to solve the problem formulated in

(8). The complexity of the multicell Max-Min algorithm is

O(

RM4N)

, where R is the total number of bits allocatedto all SUs. Obviously, the computational complexity of the

algorithm is too high to be applied in practical CR systems.

We consider the problem formulated in (8) as a non-

cooperative game in our previous work [12] and propose an

iterative algorithm which decomposes (8) into m independentsub-problem. Using iterative method to update interference

level of each CR system makes the interference constrains

to be satisfied while maximizing the sum capacity of the CR

system. Moreover, in this work, we develop a more efficient

algorithm with better performance and lower complexity.

A. MLWF Optimization Model

From (8), we can see that the constraint C1 is independentfor each CR cell while the constraints C2 is not. Withoutloss of generality, suppose each SU m on subchannel n has avirtual power spectral mask (PSM) pUm,n which can keep thethe constraint C2 satisfied in (8). We rewrite the optimizationproblem as

maxM

m=1 Rm

s.t. C1 :N

n=1 pm,n Pm, m M

C2 : 0 pm,n pUm,n, m M, n N

(9)

where Rm =N

n=1 rm,n is the sum rate of cell m. To meetthe interference constraint C2 in (8), we have

M

m=1

N

n=1

pUm,nISPm,l,n I

Ul , l L (10)

We firstly solve the optimization problem (9) and then use

MLWF algorithm to ensure (10) by a power (bits) adjustment

procedure. We propose to use Lagrangian multipliers to model

the problem (9).

Define the Lagrangian

L ({pm,n}) =M

m=1

{

N

n=1rm,n m

(

N

n=1pm,n Pm

)

N

n=1m,n(pm,n p

Um,n) +

N

n=1m,npm,n

}

(11)

where {m}m=1,...,M ,and {m,n, m,n}m=1,...,M,n=1,...,N arenonnegative Lagrangian multipliers. Based on Karush-Kuhn-

Tucker (KKT) conditions, we obtain the following results.

The transmit power allocated to subchannel n for user m isgiven by

pm,n = (1/(m + m,n) 1/(m,n))+, (12)

where ()+ denotes max{, 0}, and m,n = m/Hm,n. Here,dual variables m and m,n control the waterfilling level of

SU m on subchannel n. Since m,n changes with n, each SUm has many WF levels.

Generally, to account for the transmit power and the PSM

constraints C2 in (9), following iterations based on sub-gradient search may be implemented

k+1m =km m(Pm

N

n=1

pm,n) (13)

k+1m,n =km,n m

(

pUm,n pm,n)

(14)

where 0 m 1 is a gradient search step size, and km andkm,n denote the values of m and m,n at the kth step, re-spectively. Moreover, this approach converges in theory when

the dual update stepsize m is small enough [13]. However,gradient-based search method has a very slow convergence

due to the large number of dual variables involved. To over-

come this problem, we design a multicell cooperative MLWF

algorithm which can achieve a fast and stable convergence.

B. Multicell MLWF Algorithm

We adopt a cooperative manner to allocate the power

among all subchannels. First, we use the waterfilling algorithm

to allocate the total power Pm in each cell while keepingpm,n pUm,n. If the solution already satisfies the constraints(10), we can directly obtain the power allocation for problem

(8). Otherwise, we cooperatively adjust the power (bits) to

mitigate the interference introduced by SUs to PUs.

Similar to the Levin-Campello loading [14], the MLWF al-

gorithm also maintains an incremental energy table for discrete

power (bits) adjustment procedure. With as the granularityof the discrete bits ( = 1 for integer bits or = 0.5 fora complex channel quadrature amplitude modulation signal).

Assume user ms current bit distribution is rm,n. The energyrequired to maintain the bit distribution on subchannel n ofuser m is calculated as [15]

nm(rm,n) = 2(m/Hm,n)(2rm,n 1). (15)

The incremental energy enm to load an additional bit onsubchannel n of user m is thus

enm(rm,n) = (m/Hm,n)2rm,n+1(2 1). (16)

The pseudo-code of the multicell cooperative MLWF al-

gorithm is in Table I. The third step of the algorithm is the

fixed-margin version of the greedy bit-loading procedures by

exploiting waterfilling. The fifth step performs the multicell

cooperative power (bits) adjustment procedure to reduce the

mutual interference from SUs to PUs. The key idea of this

step is to move the power (bits) for one subchannel with high

interference to PUs to the other one which generates lower

interference to PUs until the power allocation scheme satisfied

the interference constraint (10). Obviously, the main computa-

tional loads lie on the greedy power allocation procedure and

multi-level cooperative power (bits) adjustment procedure.

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TABLE ITHE PSEUDO-CODE OF MLWF ALGORITHM

Algorithm: Multicell Cooperative MLWF Algorithm

Step 1:Initialize

1:Set rm,n 0, nm(rm,n) 0, pm,n 0, m M,

n N . Given Pm.

2:Calculate the ISPm,l,n

,IPSl,m,n

and IPSm,n respectively by (2),

(3),(4). And compute enm(rm,n + 1), m M,n N .

3:flag=1;

4:while(flag==1)

step 2:Calculate the SINR

5: Calculate the SINR by (5);

step 3:Greedy power allocation procedure

6: for m = 1 to M

7: Perform the waterfilling algorithm with Pm constraints

and obtain the pm,n and rm,n;

8: end for

step 4:Test the interference constraint

9: if the constraint (10) is met

10: flag=0, break;

11: end if

step 5: Multi-level Cooperative Power (bits) Adjustment

12: for n = 1 to N

13: g argmax(m,pm,nPm){

pm,nIm,l,n}

, m M;

14: h argmin(m,pm,nPm){

pm,nIm,l,n}

, m M;

15: if (h + eng (rg,n) e

nh(rh,n)) Ph &&

16: (g + enh(rh,n) eng (rg,n)) Pg

17: pg,n pg,n + enh(rh,n) eng (rg,n);

18: ph,n ph,n + eng (rh,n) e

nh(rh,n);

19: rg,n rg,n 1, rh,n rh,n + 1;

20: end if

21: end for

22:end while

TABLE IICOMPUTATIONAL COMPLEXITY COMPARISON

Algorithm Complexity

Exhaustive Search O(eMN )

Multicell Max-Min O(

RM4N)

Iterative algorithm O(M2N log2 N)

MLWF O(MNlog2N)

C. On the Complexity and Convergence

The MLWF greedy power allocation procedure and the

multi-level cooperative power (bits) adjustment, the dominated

parts of the whole algorithm, have the same complexity

which is equal to O(N logN) where N is the number ofsubchannels. MLWF contains a simple line-search with bi-

section or diminishing step size and thus adds logN searchsteps to each bit adjustment procedure. For M CR cells,the MLWF adds a linear complexity with regard to the Mcoordinates to be searched. Therefore the total complexity of

the MLWF algorithm is O(MNlog2N). Table II comparesthe complexity of the MLWF algorithm with other resource

allocation algorithms. R is the total bits allocated to all SUs.From Table II, we can observe the complexity of the MLWF

algorithm is the lowest compared to the others.

We analyze the convergence of the MLWF briefly. In

theory, if we take an iterative method using the (13) and

(14), the algorithm converges slowly. In practical, the MLWF

0.001 0.01 0.1 1.0 2.0 4.02

4

6

8

10

12

14

Transmit power constraint of SUs (W)

Ave

rage B

its p

er

subca

rrie

r

Average Bits Per Subcarrier

MLWF

MultiCell MaxMin

Iterative Algorithm

Fig. 2. Average bits per subcarrier as a function of power limit

can approach to solution more closely after each adjustment.

Since the solution can be always improved to maintain the

interference constraints by reducing the mutual interference

in each adjustment procedure, the solution can be found after

certain number of adjustments.

IV. SIMULATION AND DISCUSSION

We conduct a series of experiments to assess the perfor-

mance of our proposed multicell multi-level waterfilling algo-

rithm. Consider an OFDM-based multicell CR system where a

primary cell with two PUs and three CR cells coexist. All users

are located within a 3 3 km areas. The primary base stationis in the middle of the area and the secondary base stations are

randomly distributed. Each PU or SU is uniformly distributed

within a 500-meter circle of its corresponding base station.The path loss exponent is 4, the variance of the shadowingeffect is 10 dB, and the multipath fading is assumed to beRayleigh [16]. There are 16 subchannels. The noise powerof each subchannel is set to 1013W. The frequency bandsoccupied by PUs are generated randomly with the maximum

number of OFDM subchannels is 2N3 . The transmission power

of a PU is equal to the number of OFDM subchannel within

the PUs band and the interference threshold of all PUs are

set to 5 1013 W. The results presented in this section isobtained from over 1000 Monte Carlo simulations.To evaluate the performance of the MLWF, we compare

the average bits per subchannel of the MLWF with other two

schemes: Multicell Max-Min [10] and iterative algorithm [12].

Fig.2 illustrates the average bits per subchannel as a function

of the transmit power limit. It can be seen that the capacity

of all algorithm increase as the transmit power limit increases.

The solution obtained by the MLWF is better than the others,

suggesting that cooperative power allocation can achieve more

capacity than the greedy-like algorithms.

Fig.3 shows the time complexity of the three algorithms

mentioned above. The elapsed time is counted by the inbuilt

function tic-toc in Matlab. We can see the complexity of

the MLWF is much lower than the other algorithms just

as the analysis in section III. Moreover, when the transmit

power constraint of the SU (PSU) is small, greedy power

allocation procedure (step 3 in algorithm) dominates the whole

elapsed time because it needs more time to find the water

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5

0.001 0.01 0.1 1.0 2.0 4.0 10.010

4

103

102

101

100

101

Average Time Elapsed

Transmit power constraint of SUs (W)

Ave

rage T

ime E

lapse

d

MLWF

MultiCell MaxMin

Iterative Algorithm

Fig. 3. Average time elapsed as a function of power limit

0.001 0.01 0.1 1.0 2.0 4.0 10.00

0.5

1

1.5

2

2.5

3

3.5

4

Transmit power constraint of SUs (W)

Ave

rage N

um

ber

of A

dju

stm

ents

Average Number of Adjustments

Fig. 4. Average number of adjustments as a function of power limit

level while no power (bits) adjustment is required [see Fig.4].

However, when PSU is large enough, cooperative power (bits)

adjustment (step 5 in algorithm) need to be performed many

times to meet the interference-temperature constraint resulting

more time consumption [see Fig.4 and Fig.5(b)]. Naturally,

if the PSU is appropriate, there is no need to require the

adjustment procedure [see Fig.4 and Fig.5(a)] and greedy

power allocation procedure does less iterations. As analysis

above, it is reasonable to see the elapsed time of MLWF is

lower at the point of PSU= 0.1.

Finally, we investigate the convergence of the MLWF. As

discussed in section III, one of the main computational loads

of the MLWF lies in the number of the adjustment procedure.

From Fig.4 and Fig.5, we observe the average number of the

adjustment procedure lies in a narrow range [0, 4] and therandom instance total adjustment lies in [0,30]. Conservatively,

we conclude the MLWF method is effective and efficient

according to the complexity and convergence analysis in

section III.

V. CONCLUSION

In this paper we studied the resource allocation problem

in a multicell OFDM-based CR system. We try to maximize

the sum capacity of the system under transmission power and

interference constraints. An efficient and effective multilevel

waterfilling (MLWF) algorithm is developed by jointly con-

sidering the co-channel and mutual interference. The proposed

algorithm achieves better capacity performance with a lower

complexity, comparing to other existing algorithms. Besides,

0 10 20 30 40 50 60 70 80 90 1001

0.5

0

0.5

1

Nu

mb

er

of A

dju

stm

en

ts

Random instance (a)

PSU = 0.1

Times of Adjustments :PSU = 0.1

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

Nu

mb

er

of A

dju

stm

en

ts

Random instance (b)

PSU= 10.0

Times of Adjustments : PSU = 10.0

Fig. 5. Adjustments as a function of power limit

our proposed MLWF algorithm always converges fast and

stably, which makes it promising for practical applications.

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